{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "# 伽辽金有限元法重解例题 3 ([1] P.275)\n",
    "\n",
    "\n",
    "本例用有限元解法求解，并和里兹法、伽辽金法对比。\n",
    "\n",
    "用的方法是文献[2] P.186，P.248，P.250，P.253 的知识点。\n",
    "\n",
    "\n",
    "*****\n",
    "\n",
    "对应的本征值问题为求 $\\lambda$ 和\n",
    "\n",
    "$$y''(x) - \\lambda y(x) =0$$\n",
    "$$y(0) = 0,\\ y(1) = 0 $$\n",
    "\n",
    "对应的变分特征值问题为\n",
    "\n",
    "$$\n",
    "u \\in S_0^1 ,\\ u(x) \\ne 0 \\\\\n",
    "$$\n",
    "\n",
    "$$\n",
    "D(u,v) = \\lambda *(u,v) , \\forall v \\in S_0^1\n",
    "$$\n",
    "\n",
    "\n",
    "其中 \n",
    "$$D(u,v) = \\int_0^1 \\frac{\\mathrm{d} u} {\\mathrm{d} x}\\frac{\\mathrm{d} v} {\\mathrm{d} x} \\mathrm{d} x$$ \n",
    "\n",
    "*****\n",
    "\n",
    "需要计算的矩阵有\n",
    "\n",
    "$$A^{(h)}=[a_{ij}]\\in\\mathbb{R}^{(n-1)\\times(n-1)},\\quad a_{ij}=D(\\phi_{i},\\phi_{j}),$$\n",
    "$$B^{(h)}=[b_{ij}]\\in\\mathbb{R}^{(n-1)\\times(n-1)},\\quad b_{ij}=(\\phi_{i},\\phi_{j}) =\\int_0^1 u v \\mathrm{d} x .$$\n",
    "\n",
    "基函数为：\n",
    "\n",
    "$$\\phi_0(x)=\\begin{cases}\\frac{x_1-x}{h_1},&x_0\\leqslant x<x_1,\\\\\n",
    "0,&x_1\\leqslant x\\leqslant x_N,\\end{cases}$$\n",
    "\n",
    "$$\\phi_i(x)=\\begin{cases}0,&x_0\\leqslant x<x_{i-1},\\\\[2ex]\n",
    "\\frac{x-x_{i-1}}{h_i},&x_{i-1}\\leqslant x<x_i,\\\\[2ex]\\frac{x_{i+1}-x}{h_{i+1}},&x_i\\leqslant x<x_{i+1},\\\\[2ex]0,&x_{i+1}\\leqslant x\\leqslant x_N,\\end{cases}\\quad i=1,2,\\cdots,N-1,$$\n",
    "\n",
    "$$\\phi_N(x)=\\begin{cases}0,&x_0\\leqslant x<x_{N-1},\\\\[2ex]\\frac{x-x_{N-1}}{h_N},&x_{N-1}\\leqslant x\\leqslant x_N.\\end{cases}$$\n",
    "\n",
    "\n",
    "******\n",
    "\n",
    "最终要求解的本征值方程为：\n",
    "\n",
    "$$ A^{(h)} u = \\lambda^{h} B^{(h)} u $$\n",
    "\n",
    "******\n",
    "\n",
    "\n",
    "参考书\n",
    "\n",
    "[1] 姚端正、周国全、贾俊基《数学物理方法》第4版\n",
    "\n",
    "[2] 陆金甫、关冶 《偏微分方程数值解法》第3版 \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b0f74b2-86df-4e0d-b78c-0f7aa49ac37d",
   "metadata": {},
   "source": [
    "## 1、导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sy  # 导入sympy 包中所有的函数\n",
    "from sympy.abc import x,y # 引入默认的符号变量\n",
    "from scipy.sparse import dia_matrix \n",
    "from scipy.sparse.linalg import inv, eigsh\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c523a70",
   "metadata": {},
   "source": [
    "## 2、 定义基函数计算矩阵元\n",
    "\n",
    "我们计划用sympy来进行微积分运算，我们先考虑最简单的情景，所有的自变量的步长为 $h$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d2501d80",
   "metadata": {},
   "outputs": [],
   "source": [
    "xjm1, xj, xjp1 = sy.symbols(['x_{j-1}', 'x_{j}', 'x_{j+1}'])\n",
    "x, h, eps = sy.symbols(['x', 'h', '\\epsilon'])\n",
    "\n",
    "phi_l =  (x - xj + h)/h\n",
    "phi_r =  (xj + h -x)/h\n",
    "\n",
    "b_i_im1 = sy.integrate((xj  - x)/h * phi_l, (x, xj - h, xj)).simplify()\n",
    "b_i_ip1 = sy.integrate((x - xj)/h * phi_r, (x, xj, xj+h)).simplify()\n",
    "b_i_i   = (sy.integrate(phi_l *phi_l , (x, xj-h, xj)) + sy.integrate(phi_r*phi_r , (x, xj, xj+h))).simplify()\n",
    "b_0_0 =  sy.integrate((h - x)/h*(h - x)/h, (x, 0, h)).simplify()\n",
    "b_N_N = sy.integrate(phi_l *(x - xj+h)/h , (x, xj-h, xj)).simplify()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adcd0e87-4638-415d-970a-e0492c419f21",
   "metadata": {},
   "source": [
    "展示计算结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c070e70a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h}{3}$"
      ],
      "text/plain": [
       "h/3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_0_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7df1d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h}{6}$"
      ],
      "text/plain": [
       "h/6"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_i_ip1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7836e54b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 h}{3}$"
      ],
      "text/plain": [
       "2*h/3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_i_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "571e6201",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h}{6}$"
      ],
      "text/plain": [
       "h/6"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_i_im1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ed843270",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h}{3}$"
      ],
      "text/plain": [
       "h/3"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_N_N"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fe0c96f-630b-409b-ba5f-9babc5cf897d",
   "metadata": {},
   "source": [
    "## 3、定义稀疏矩阵。\n",
    "\n",
    "参看文献[2] P.254."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ee6933f-d63d-45d9-bf17-0930ab30bf09",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1000\n",
    "m =  np.ones(n)\n",
    "data1 = [-m, 2*m, -m]\n",
    "offsets = [-1, 0, 1]\n",
    "# 使用 scipy.sparse 稀疏矩阵库，\n",
    "A = dia_matrix((data1, offsets), shape=(n, n), dtype = float).tocsc() \n",
    "data2 = [m/6, 4*m/6, m/6]\n",
    "B = dia_matrix((data2, offsets), shape=(n, n), dtype = float).tocsc()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "84a9c497",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.66666667, 0.16666667, 0.        , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.16666667, 0.66666667, 0.16666667, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.16666667, 0.66666667, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.        , ..., 0.66666667, 0.16666667,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.16666667, 0.66666667,\n",
       "        0.16666667],\n",
       "       [0.        , 0.        , 0.        , ..., 0.        , 0.16666667,\n",
       "        0.66666667]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.toarray() # 查看矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "870bdeaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2., -1.,  0., ...,  0.,  0.,  0.],\n",
       "       [-1.,  2., -1., ...,  0.,  0.,  0.],\n",
       "       [ 0., -1.,  2., ...,  0.,  0.,  0.],\n",
       "       ...,\n",
       "       [ 0.,  0.,  0., ...,  2., -1.,  0.],\n",
       "       [ 0.,  0.,  0., ..., -1.,  2., -1.],\n",
       "       [ 0.,  0.,  0., ...,  0., -1.,  2.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.toarray() # 查看矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e564343b-e7cd-472b-a531-776d5610b3b9",
   "metadata": {},
   "source": [
    "## 4、求解方程。下面的矩阵计算忽略了步长 $h$，注意计算完后要回复。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b1db7b4c-a630-474c-8c8a-0e2f2e33cc43",
   "metadata": {},
   "outputs": [],
   "source": [
    "w,v=eigsh(A, k=10, M=B,which='SM')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9cea2f4e-9546-4a20-96e6-469cc7a6b2df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.84990285,  39.39970841,  88.64970775, 157.60038597,\n",
       "       246.25242223, 354.60668975, 482.6642558 , 630.42638175,\n",
       "       797.89452302, 985.07032918])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w*n**2 # 展示前十个本征值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58470599",
   "metadata": {},
   "source": [
    "## 5、画图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bd64351d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2ad750b61d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(0,1,n)\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(v[:,0]*np.sqrt(n),'o',label='ground state')\n",
    "ax.plot(np.sqrt(2) *np.sin( np.pi* x), label='exact solution')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b332db71-1604-46c4-afbe-ca7103d86c68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000032833036205"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(v[:,1]) # 查看节是否已经归一化。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b44b1fd4-4fc5-449a-b0d0-f82df234f8e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2ad750bcdd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2, ax2 = plt.subplots()\n",
    "ax2.plot(-v[:,1]*np.sqrt(n), 'o',label='second state')\n",
    "ax2.plot(np.sqrt(2) *np.sin( 2*np.pi* x), label='exact solution')\n",
    "ax2.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f958d0f3-90b6-446a-9dfa-2848795e03ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2ad7818e210>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig3, ax3 = plt.subplots()\n",
    "ax3.plot(np.sqrt(2) *np.sin( np.pi* x)-v[:,0]*np.sqrt(n),label='difference of ground state')\n",
    "ax3.plot(np.sqrt(2) *np.sin( 2*np.pi* x) +v[:,1]*np.sqrt(n), label='difference of second state')\n",
    "ax3.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "feb3ec68-ee97-4bc1-aefe-1955c6869a1a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
